Properties

Label 116886.c
Number of curves $6$
Conductor $116886$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.c1 116886b6 \([1, 1, 0, -9575216, 11400258324]\) \(54804145548726848737/637608031452\) \(1129561521807136572\) \([2]\) \(5242880\) \(2.6149\)  
116886.c2 116886b4 \([1, 1, 0, -2143396, -1208679776]\) \(614716917569296417/19093020912\) \(33824451219883632\) \([2]\) \(2621440\) \(2.2683\)  
116886.c3 116886b3 \([1, 1, 0, -613956, 168215040]\) \(14447092394873377/1439452851984\) \(2550078533913627024\) \([2, 2]\) \(2621440\) \(2.2683\)  
116886.c4 116886b2 \([1, 1, 0, -139636, -17244080]\) \(169967019783457/26337394944\) \(46658301724387584\) \([2, 2]\) \(1310720\) \(1.9218\)  
116886.c5 116886b1 \([1, 1, 0, 15244, -1477296]\) \(221115865823/664731648\) \(-1177612663062528\) \([2]\) \(655360\) \(1.5752\) \(\Gamma_0(N)\)-optimal
116886.c6 116886b5 \([1, 1, 0, 758184, 815041836]\) \(27207619911317663/177609314617308\) \(-314645735012752777788\) \([2]\) \(5242880\) \(2.6149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886.c have rank \(0\).

Complex multiplication

The elliptic curves in class 116886.c do not have complex multiplication.

Modular form 116886.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - q^{12} + 2q^{13} + q^{14} + 2q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.